Cytoskeletal identification by ILEE. (a) Visual demonstration and summarized mathematical process of ILEE. On the left, the visualized intermediate images of ILEE process are presented; on the right, an abbreviated mathematical process of ILEE is shown (gray, image pre-processing; blue, ILEE in a narrow sense; yellow, post-processing; also see Materials and methods for the detailed computational algorithm). (b) The value of implicit Laplacian smoothing coefficient K influences ILEE performance. When K is small (e.g., 2.5), the rendering of faint and thin filaments is accurate, but the edge of thick filaments tends to be omitted. Conversely, when K is large (e.g., 200), rendering of thick filaments is accurate but thin and faint filaments are omitted. A solution is applied by creating a full outer join threshold image by a fixed K₁ = 2.5 and an estimated universal K₂ for an entire biological batch of samples. (c)K₂ estimation model. A regression model to compute any universal K₂ for a given sample batch (see Fig. S10 for detail). To augment the training samples, seven images with manually portrayed binary ground truth are interpolated by a new resolution of different folds to the original, into 42 samples (shown as single dots) that cover the general range of actin thickness. A non-linear regression estimation model is trained using the highest 5% DT (distance transform) values in the ground truth (representing filament thickness) and an anticipated K₂ with a specific satisfactory capability to detect thick filament (see Fig. S10 for detail). In the standard ILEE pipeline, the mean of top 5% DT of all input samples will be calculated by Niblack thresholding to obtain the universal K₂ for ILEE. Scale bars are marked as red/yellow solid line.